MEs such as mobile telephones include a UICC which, among other things, holds secure data for identifying the user to the core network. The UICC is a smart card that has an inbuilt microprocessor and memory which can run a number of software applications. The UICC is powered by the battery within the ME. The standards setting Organisation ETSI is in the process of finalising Release 7 of its standards documents (including TS 102 221, TS 102 600 and TS 102 223) relating to the interaction between the ME and its UICC. This standards documentation specifies that the ME negotiates the maximum power supply that will be available to the UICC before any applications are selected/activated when the ME is powered up. Once defined, this maximum value is fixed until the ME is reset and, until then, the UICC is free to draw the specified maximum power at any time. The inventors have realised that this arrangement is less than optimal and can shorten the battery lifetime significantly.